Quantum correlations in complex systems (QUACOCOS) constitute a key element of modern quantum information theory. This interdisciplinary field combines many concepts and tools from various mathematical and physical areas of research, ranging from complexity theory to quantum mechanics of large systems. Quantum correlations and entanglement are at the heart of many of the possible applications of quantum information theory. They provide the potential for unconditionally secure quantum cryptography and communication, are required for measurement based quantum computation and are involved in most of the famous quantum algorithms outperforming all classical equivalents. Furthermore these correlations are also fundamental to the physics of large and complex systems. Their role in condensed matter systems, such as e.g. phase transitions, is undoubted, in ionization procedures of quantum gases is commonly accepted and their potential involvement in complex biological systems, such as e.g. DNA and light harvesting complexes, is still subject to a controversial debate.This project aims at first developing the mathematical tools required for a thorough analysis of quantum correlations and entanglement in complex systems. These shall then be used to address many open questions in the physics of large complex systems and investigate potential applications thereof in quantum information science. The results are expected to shed light on the actual role entanglement and correlations play in biological systems, condensed matter systems and quantum algorithms.